Efficient Score Statistics for Mapping Quantitative Trait Loci with Extended Pedigrees

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Abstract
The method of variance components is the method of choice for mapping quantitative trait loci (QTLs) with general pedigrees. Being a likelihood-based method, this method can be computation intensive even for nuclear families, and has excessive false positive rates under some situations. Here two efficient score statistics to detect QTLs are derived, one assumes that the candidate locus has no dominance effect, and the other one does not make such an assumption. These two score statistics are asymptotically equivalent to the method of variance components but they are easier to compute and more robust than the likelihood ratio statistic. The derivation of these score statistics is facilitated by separating the segregation parameters, the parameters that describe the distribution of the phenotypic value in the population, from the linkage parameters, the parameters that measure the effect of the candidate locus on the phenotypic value. Such a separation of the model parameters greatly reduces the number of parameters to be dealt with in the analysis of linkage. The asymptotic distributions of both score statistics are derived. Simulation studies indicate that, compared to the method of variance components, both score statistics have comparable or higher power, and their false-positive rates are closer to their respective nominal significance levels.